Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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            <s xml:id="echoid-s5351" xml:space="preserve">
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            pro axiſumptum eſt) & </s>
            <s xml:id="echoid-s5352" xml:space="preserve">curua circuli, vel ellipſis contine-
              <lb/>
            tur, erunt proximè, vt baſis eiuſdem parallelogrammi ad ſui
              <lb/>
            reliquum, demptis ab ea, {11/14}, rectæ lineæ, quæ ſit æqualis
              <lb/>
            dimidiæ ſecundæ diametri Prædicti circuli, vel ellipſis, ſi-
              <lb/>
            mul cum exceſſu, quo dicti, {11/14}, excedunt, {2/3}, tertiæ propor-
              <lb/>
            tionalis duarum, quarum prima eſt dicta baſis, ſecunda au-
              <lb/>
            tem dicta ſecundæ diametri dimidia.</s>
            <s xml:id="echoid-s5353" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5354" xml:space="preserve">Sit parallelogrammum, FD, & </s>
            <s xml:id="echoid-s5355" xml:space="preserve">circa latus, FB, vtcunque tam-
              <lb/>
            quam circa diametrum (intellige autem ſemper diametrum hic, & </s>
            <s xml:id="echoid-s5356" xml:space="preserve">
              <lb/>
            in ſequentibus, vt eſt nomen commune diametro, & </s>
            <s xml:id="echoid-s5357" xml:space="preserve">axi) integri ſic
              <lb/>
            deſcriptus ſemicirculus, vel ſemiellipſis, FQB, cuius curua, FQB,
              <lb/>
            neque tangat, neque ſecet latus, ZD, oppoſitum lateri, FB, bifa-
              <lb/>
            riam autem diuiſa, FB, in, A, & </s>
            <s xml:id="echoid-s5358" xml:space="preserve">per, A, ipſi, BD, baſi ducta pa-
              <lb/>
            rallela, AP, ſeceturà curua, FQB, vtcunq; </s>
            <s xml:id="echoid-s5359" xml:space="preserve">in, Q; </s>
            <s xml:id="echoid-s5360" xml:space="preserve">erit autem, A
              <lb/>
            Q, dimidia ſecundæ axis circuli, vel ellipſis, cuius centrum, A; </s>
            <s xml:id="echoid-s5361" xml:space="preserve">du-
              <lb/>
            catur inſuperper, Q, ipſi, FB, parallela, HC, quæ tanget circu-
              <lb/>
              <note position="left" xlink:label="note-0240-01" xlink:href="note-0240-01a" xml:space="preserve">17.1.Con.</note>
            lum dictum, vel ellipſim, & </s>
            <s xml:id="echoid-s5362" xml:space="preserve">erit, BC, æqualis ipſi, AQ; </s>
            <s xml:id="echoid-s5363" xml:space="preserve">fiat dein-
              <lb/>
            de, vt, DB, ad, BC, ita, BC, ad, BI, & </s>
            <s xml:id="echoid-s5364" xml:space="preserve">ſumatur, BR, quæ ſit,
              <lb/>
            {2/3}, BI, &</s>
            <s xml:id="echoid-s5365" xml:space="preserve">, BE, quæ fit, {11/14}, ipſius, CB, &</s>
            <s xml:id="echoid-s5366" xml:space="preserve">, EV, quæ ſit æqualis
              <lb/>
              <figure xlink:label="fig-0240-01" xlink:href="fig-0240-01a" number="150">
                <image file="0240-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0240-01"/>
              </figure>
            ipſi, ER, regula verò ſit, BD. </s>
            <s xml:id="echoid-s5367" xml:space="preserve">Dico er-
              <lb/>
            go omnia quadrata parallelogrammi, FD,
              <lb/>
            ad omnia quadrata figuræ, quæ compre-
              <lb/>
            henditur tribus lateribus, FZ, ZD, DB,
              <lb/>
            & </s>
            <s xml:id="echoid-s5368" xml:space="preserve">curua, FQB, eſſe, vt, BD, ad, DV,
              <lb/>
            proximè. </s>
            <s xml:id="echoid-s5369" xml:space="preserve">Omnia .</s>
            <s xml:id="echoid-s5370" xml:space="preserve">n. </s>
            <s xml:id="echoid-s5371" xml:space="preserve">quadrata parallelo-
              <lb/>
            grammi, FD, ad rectangula ſub paralle-
              <lb/>
            logrammo, FD, & </s>
            <s xml:id="echoid-s5372" xml:space="preserve">ſemicirculo, vel ſemi-
              <lb/>
              <note position="left" xlink:label="note-0240-02" xlink:href="note-0240-02a" xml:space="preserve">Coroll.1.
                <lb/>
              26.lib.2.</note>
            ellipſis, FQB, ſunt vt parallelogram-
              <lb/>
            mum, FD, ad eundem ſemicirculum, vel
              <lb/>
            ſemiellipſim, FQB; </s>
            <s xml:id="echoid-s5373" xml:space="preserve">quia verò parallelo-
              <lb/>
            grammum, FD, ad parallelogrammum, FC, eſt vt, DB, ad, BC,
              <lb/>
            & </s>
            <s xml:id="echoid-s5374" xml:space="preserve">item parallelogrammum, FC, ad ſemicirculum, vel ſemiellipſim,
              <lb/>
              <note position="left" xlink:label="note-0240-03" xlink:href="note-0240-03a" xml:space="preserve">5. Lib.2.
                <lb/>
              Arch. de
                <lb/>
              Dim.Cir.</note>
            FQB, eſt proximè vt 14. </s>
            <s xml:id="echoid-s5375" xml:space="preserve">ad 11. </s>
            <s xml:id="echoid-s5376" xml:space="preserve">ideſt vt, CB, ad, BE, ergo ex
              <lb/>
            æquali parallelogrammum, FD, ad ſemicirculum, vel ſemiellipſim,
              <lb/>
            FQB, erit vt, DB, ad, BE, & </s>
            <s xml:id="echoid-s5377" xml:space="preserve">ideò omnia quadrata parallelogram-
              <lb/>
            mi, FD, ad rectangula ſub parallelogrammo, FD, & </s>
            <s xml:id="echoid-s5378" xml:space="preserve">ſemicirculo,
              <lb/>
              <note position="left" xlink:label="note-0240-04" xlink:href="note-0240-04a" xml:space="preserve">5.Lib.2.</note>
            vel ſemiellipſi, FQB, erunt vt, DB, ad, BE,.</s>
            <s xml:id="echoid-s5379" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5380" xml:space="preserve">ſumpta, DB, com-
              <lb/>
            muni altitudine erunt, vt quadratum, DB, ad rectangulum ſub, D
              <lb/>
            B, BE, quodſerua.</s>
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          <p>
            <s xml:id="echoid-s5382" xml:space="preserve">Aduerte nunc, quodrectangula ſub parallelogrammo, FD, & </s>
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